Phân tích đa thức thành nhân tử
a/ \(ax-bx+ab-x^2\)
b/ \(x^2-2xy+y^2-9\)
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TL
1
13 tháng 12 2022
a: =x(4x^2+4x+1)
=x(2x+1)^2
b: =(x-y)^2-49
=(x-y-7)(x-y+7)
NN
16 tháng 10 2021
a,x^2-x-y^2-y
=x^2-y^2-(x+y)
=(x-y).(x+y)-(x+y)
=(x+y).(x-y-1)
b, x^2-2xy+y^2-z^2
=(x^2-2xy+y^2)-z^2
=(x-y)^2-z^2
=(x-y-z)(x-y+z)
c,5x-5y+ax-ay( đề bài ở đây phải là -ay ms tính đc)
=(5x-5y)+(ax-ay)
=5(x-y)+a(x-y)
=(x-y).(5+a)
d,a^3-a^2.x-ay+xy
=(a^3-a^2x)-(ay-xy)
=a^2(a-x)-y(a-x)
=(a-x)(a^2-y)
e,4x^2-y^2+4x+1
={(2x)^2+4x+1}-y^2
=(2x+1)^2-y^2
=(2x+1+y^2)(2x+1-y^2)
f,x^3-x+y^3-y
=(x^3+y^3)-(x+y)
=(x+y)(x^2-xy+y^2)-(x+y)
=(x+y)(x^2-xy+y^2-1)
LN
1
PL
15 tháng 7 2018
ax - ay + bx - by= (ax - ay) + (bx - by)
= a(x - y) + b(x - y)
= (x - y)(a + b)
x2 - 2xy + y2 - 1= (x2 - 2xy + y2) - 12
= (x - y)2 - 12
= (x - y - 1)(x - y + 1)
9 - x2 - 2xy - y2 = 32 - ( x2 + 2xy + y2 )
= 32 - ( x + y)2
= ( 3 - ( x + y)).(3 + ( x + y))
= (3 - x - y)(3 + x + y)
20 tháng 10 2021
b: \(x^2-6x+xy-6y\)
\(=x\left(x-6\right)+y\left(x-6\right)\)
\(=\left(x-6\right)\left(x+y\right)\)
c: \(2x^2+2xy-x-y\)
\(=2x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(2x-1\right)\)
e: \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
22 tháng 10 2023
2:
a: \(x^2-12x+20\)
\(=x^2-2x-10x+20\)
=x(x-2)-10(x-2)
=(x-2)(x-10)
b: \(2x^2-x-15\)
=2x^2-6x+5x-15
=2x(x-3)+5(x-3)
=(x-3)(2x+5)
c: \(x^3-x^2+x-1\)
=x^2(x-1)+(x-1)
=(x-1)(x^2+1)
d: \(2x^3-5x-6\)
\(=2x^3-4x^2+4x^2-8x+3x-6\)
\(=2x^2\left(x-2\right)+4x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(2x^2+4x+3\right)\)
e: \(4y^4+1\)
\(=4y^4+4y^2+1-4y^2\)
\(=\left(2y^2+1\right)^2-\left(2y\right)^2\)
\(=\left(2y^2+1-2y\right)\left(2y^2+1+2y\right)\)
f; \(x^7+x^5+x^3\)
\(=x^3\left(x^4+x^2+1\right)\)
\(=x^3\left(x^4+2x^2+1-x^2\right)\)
\(=x^3\left[\left(x^2+1\right)^2-x^2\right]\)
\(=x^3\left(x^2-x+1\right)\left(x^2+x+1\right)\)
g: \(\left(x^2+x\right)^2-5\left(x^2+x\right)+6\)
\(=\left(x^2+x\right)^2-2\left(x^2+x\right)-3\left(x^2+x\right)+6\)
\(=\left(x^2+x\right)\left(x^2+x-2\right)-3\left(x^2+x-2\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x-3\right)\)
\(=\left(x^2+x-3\right)\left(x+2\right)\left(x-1\right)\)
h: \(\left(x^2+2x\right)^2-2\left(x+1\right)^2-1\)
\(=\left(x^2+2x+1-1\right)^2-2\left(x+1\right)^2-1\)
\(=\left[\left(x+1\right)^2-1\right]^2-2\left(x+1\right)^2-1\)
\(=\left(x+1\right)^4-2\left(x+1\right)^2+1-2\left(x+1\right)^2-1\)
\(=\left(x+1\right)^4-4\left(x+1\right)^2\)
\(=\left(x+1\right)^2\left[\left(x+1\right)^2-4\right]\)
\(=\left(x+1\right)^2\left(x+1+2\right)\left(x+1-2\right)\)
\(=\left(x+1\right)^2\cdot\left(x+3\right)\left(x-1\right)\)
i: \(x^2+4xy+4y^2-4\left(x+2y\right)+3\)
\(=\left(x+2y\right)^2-4\left(x+2y\right)+3\)
\(=\left(x+2y\right)^2-\left(x+2y\right)-3\left(x+2y\right)+3\)
\(=\left(x+2y\right)\left(x+2y-1\right)-3\left(x+2y-1\right)\)
\(=\left(x+2y-1\right)\left(x+2y-3\right)\)
j: \(x\cdot\left(x+1\right)\left(x+2\right)\left(x+3\right)-3\)
\(=\left(x^2-3x\right)\left(x^2-3x+2\right)-3\)
\(=\left(x^2-3x\right)^2+2\left(x^2-3x\right)-3\)
\(=\left(x^2-3x+3\right)\left(x^2-3x-1\right)\)
LP
21 tháng 12 2021
a)\(=\left(x^2+2x+1\right)-y^2=\left(x+1\right)^2-y^2=\left(x+1+y\right)\left(x+1-y\right)\)
b)\(=\left(x+9\right)^2-\left(6x\right)^2=\left(x+9-6x\right)\left(x+9+6x\right)=\left(-5x+9\right)\left(7x+9\right)\)
c)\(=\left(x^2-2xy+y^2\right)-\left(z^2-2zt+t^2\right)=\left(x-y\right)^2-\left(z-t\right)^2\\ =\left(x-y+z-t\right)\left(x-y-z+t\right)\)
10 tháng 10 2016
a) \(ax+ay-3x-3y=a\left(x+y\right)-3\left(x+y\right)=\left(a-3\right)\left(x+y\right)\)
b) \(x^3-3x^2+3x-9=x^2\left(x-3\right)+3\left(x-3\right)=\left(x-3\right)\left(x^2+3\right)\)
c) xem lại đề
d) \(9-x^2-2xy-y^2=9-\left(x+y\right)^2=\left(3-x-y\right)\left(3+x+y\right)\)
12 tháng 9 2015
a)x^2+2x-4y^2-4y
=(x2-4y2)+(2x-4y)
=(x-2y)(x+2y)+2.(x-2y)
=(x-2y)(x+2y+2)
b)x^4-6x^3+54x-81
=(x4-81)+(-6x3+54x)
=(x2-9)(x2+9)-6x.(x2-9)
=(x2-9)(x2+9-6x)
=(x-3)(x+3)(x-3)2
=(x-3)3(x+3)
c)ax^2+ax-bx^2-bx-a+b
=(ax2-bx2)+(ax-bx)+(-a+b)
=x2.(a-b)+x.(a-b)-(a-b)
=(a-b)(x2+x+1)
TV
2
6 tháng 1 2022
a: =2(x-2)+y(x-2)
=(x-2)(2+y)
b: \(=\left(x+y\right)^2-4=\left(x+y+2\right)\left(x+y-2\right)\)
c: =(x-7)(x+2)
6 tháng 1 2022
a.
2x - 4 + xy - 2y
= 2(x-2) +y(x-2)
= (x-2)(y+2)
c.
x^2 - 5x - 14
= x^2 + 2x - 7x - 14
= x(x+2) - 7(x+2)
= (x-7)(x+2)
a) \(ax-bx+ab-x^2=\left(ax+ab\right)-\left(bx+x^2\right)=a\left(x+b\right)-x\left(x+b\right)=\left(x+b\right)\left(a-x\right).\)
b) \(x^2-2xy+y^2-9=\left(x^2-2xy+y^2\right)-3^2=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x+y+3\right).\)
Học tốt nhé ^3^
\(a.=a\left(x+b\right)-x\left(b+x\right)\)
\(=a\left(x+b\right)-x\left(x+b\right)\)
\(=\left(a-x\right)\left(x+b\right)\)
\(b.=\left(x-y\right)^2-3^2\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
_Moon_